Physics 7B - ABLecture 1

Lecturer Dr. Yu Sato111 Phy/GeoWed 4-5pm

sato@physics.ucdavis.edu** When using e-mail, please include “Physics7B” in the subject line. **

Lecture slides available athttp://physics.ucdavis.edu/physics7

Course Websitehttp://physics.ucdavis.edu/physics7

Click on Physics 7B-A/B

Lecturer 3Dr. Kevin Klapstein

Course Policy Highlights

Text College Physics: A Models Approach, Part II by W. PotterTextDiscussion/Lab Workbook

Final Examination June 9, Monday, 1pm – 3pm

Course Grading = Exam grade +/- DL grade.

Exam grade (8 quizzes and the final)D/L grade

Your quiz grade is the average of five highest individual quiz grades. Your Exam grade is then the higher of either of the two weighting schemes.

(a) 50% Quiz grade + 50% Final grade(b) 20%Quiz grade + 80% Final grade

Bring to your DL meetings!

Six Quizzes during lectures

Go to your assigned lecture timeFull schedule of Quizzes this quarter on the academic calendar on the website.Consult Quiz information on the website for (given) Quizzes, solution, rubrics, and grades.

Q R S T

Be sure to write your name, ID number & DL section!!!!!

We categorise/grade your responses based on :(1) your understanding of the problem(2) choice of appropriate model(3) logic to arrive at the (hopefully correct) answer.

Rubric Codes

Attendance in the DL(Discussion/Lab) section is

MANDATORY

• With two unexcused DL absences, your highest DL grade is a low pass (lowers your grade by 0.5 pts). • With three unexcused DL absences, your DL grade is unsatisfactory (lowers your grade by 2 pts). In case of emergency… As the space is limited in Walker Annex 114, you should also contact the make-up DL instructor before the make-up DL to ensure extra space will be available for you. Consult the link “DL Meeting Times” and the academic calendar on the website for the full schedule and the list of DL instructors/their e-mail addresses.

Academic Dishonesty

• Copying during quizzes/final.• Taking a test for another student.• Modifying a quiz before asking for a re-grade.

Suspected cheating of any form is always reported to Student Judicial Affair for appropriate action.

All DLs are in 114 Walker Annex

Second DL (DLM 2) starts TODAY

This is 114 Walker TB

All DLs are in 114 Walker Annex

Second DL (DLM 2) starts TODAY

IMPORTANTOnly the DL instructor of the section you want to add is able to issue

you a PTA number.

DL meeting times (list of DL instructors with e-mail addresses) posted on the website

Currently, 21 waitlisted.

What is physics 7?Physics 7 is a 3-quarter series of physics classes, typically taken by bio-science and other non-physical science majors.

• Physics 7A: Energy conservation, thermodynamics, particle models of matter… • Physics 7B: Fluids, Electricity, Classical Mechanics (Newtonian Model), rotational motion, conservation of angular momentum, common kinds of change.• Physics 7C: Wave phenomena, optics, electricity and magnetism, the atom and modern quantum mechanics.

ModelsUseful way to think of and address

questions about phenomena(e.g. Energy interaction model)

Models in Physics 7BModels can help us organize our thinking, and can be very useful.

Models also have limitations: experiment is the final judge.• Energy Density Model (Fluids)• Linear Transport Model (Fluids, Circuits)

• Gallilean Space-Time Model We can understand our universe in 3D + Time and 3 spatial dimensions and time are all independent of each other.We now know (Thanks to Einstein et al.) this is NOT true but

very usefulto analyze many physical phenomena. • Force model • Momentum Conservation Model• Angular Momentum Model• Newtonian Model

• Exponential Change Model

Hum…I already know this one!

“Learning” Physics 7B

You learn music, soccer, ski,physics, etc. by practicing under the watchful eyes of your instructor/coach. You learn the basic ideas and practice with them, and then you go out there and apply them in complex situations.

Physics 7 : 1.4 hours practice in lecture + 5 hrs of practice in DL ++ 2-4 hrs of practice at home (FNTs/review) = 9-10 hrs

OK… how do we “practice” ?Learn basic physical models

Be able to explain physical ideas in common English, in technical scientificEnglish, and in mathematics (calculate measurable quantities). Be able to use these models to explain/calculate in new situations

Don’ts Don’t learn the answers

Do’s Learn how to use the model to find answers

Lecture 1Steady-State Energy Density Model

Applied to Fluid Circuit

Electrical Circuit

What is Fluid?

Gasses, Liquids.

Individual molecules do not have fixed positions relative to each other.

How do we characterize Fluid?

Volume, Temperature, Pressure…

UCDavis, sea level, 103 kPa, 1 Pascal = 1N/m2

Mt.Everest, 8848m, 30 kPa

How do we analyze Steady State Motion of a fluid?

Example: Blood flowing in your circulatory system (arteries, capillaries and veins)

Generally, Q = 0, but this volume of fluid is still an open system . Why? The fluid behind it (on the right of it) is pushing it to the left (so work energy is added) and it is pushing to the left on the fluid ahead of it (so work energy is remo ved) .

We must choose a system to analyze, so focus on a small part of the fluid ( volume = V i) as it is pushed through the pipe from th e right side to the left side (ignore the very very small volume in the capillary).

Pressure = P i = P2 Pressure = P f = P1

initial Vi

final Vf

How do we analyze a Steady-State Motion of a fluid?

Heart

How do we analyze Steady State Motion of a fluid?

Example: Blood flowing in your circulatory system (arteries, capillaries and veins)

Generally, Q = 0, but this volume of fluid is still an open system . Why? The fluid behind it (on the right of it) is pushing it to the left (so work energy is added) and it is pushing to the left on the fluid ahead of it (so work energy is remo ved) .

We must choose a system to analyze, so focus on a small part of the fluid ( volume = V i) as it is pushed through the pipe from th e right side to the left side (ignore the very very small volume in the capillary).

Pressure = P i = P2 Pressure = P f = P1

initial Vi

final Vf

By conserving energy, Of Course!

Use energy conservation for this open system (we will always have Q=0) .

? =U Uf-Ui but? =U Wtotal=W fluid pushing on right+W fluid being pushed on left=PiV i-PfV f

So Uf+PfV f=Ui+PiV i( . .i e Hf=Hiso ,enthalpy is conserved? =0H in this si )tuation

Simplifications- 1) Take? =U ? Eth( . . i e no? Ebond) 2) Take Vf=Vi= ( V normal fluids are almost incompressible so the

)volume change is negligible

, Thus conservation of energy for thisopen system tells us that? =H ? Eth+V? =0P

More gene , rally the fluid can speed up or slow down and can flow uphill or downhill so the bulk KE and PEgrav can also change .and we need to include changes in these terms

, Finally we may add work energy from another source ( ).such as a pump the heart

So now w :e write? Eth+V? +P ? +KE ? PEg=Epump

:We generally divide both sides by V and rearrange terms to write the transport equation? +P ? / +KE V ? PEg/ =V -?Eth/ +V Epump/V

Use energy conservation for this open system

(we will always have Q = 0)

∆U = Uf – Ui but ∆U = Wtotal = Wfluid pushing on right + Wfluid being pushed on left = PiVi – PfVf

∆H = 0 in this situation )

∆U = ∆Eth (i.e., ∆Ebond = 0)

∆H = ∆Eth + V∆P = 0

∆Eth + V∆P + ∆KE + ∆PEg = Epump

∆P + ∆KE/V + ∆PEg/V + ∆Eth/V= Epump/V

∆P + (1/2)∆(v2) + g∆y + IR = Volumetic flow rate I : [I] = [m3/s], Resistance R : [R] = [J s/m6], : total energy/volume put in by pump

Our Model for Analyzing Fluid Flow

(use these two ideas to analyze every fluid problem)

(1) Conservation of Energy (as applied to Fluids)a.k.a. Fluid Transport Equation/Energy Density Equation/Extended Bernoulli eq.

∆P + (1/2)∆(v2) + g∆h + IR = Epump/V

*Volumetic flow rate I : [I] = [m3/s], Resistance R : [R] = [J s/m6]Don’t’s : Since the fluid is in a steady state, you don’t pick two points in time to find the changes. Do’s : Instead, pick two points in the fluid circuit to calculate changes in the various quantities.

(P2– P1) + (1/2)(v22 – v1

2) + g( h2 – h1) + IR12 = 12

IR12: Resistance of the pipe between points 1 to 2

12: total energy/volume put in (or taken out) by all the pumps between points 1 to 2

Indicator for KE is fluid speed

Conservation of Matter tells us about the speed : If 12m3 of water flows into a hose every second then 12m 3 of water must flow out of the hose every second.

So this “flow rate” of 12m 3/s (also called the “current”, I) must be constant.

Total current coming in = total current going out so IA = IB

Then how can the speed of the water ever change? Suppose a pipe has water flowing in it. We will examine the motion of 1 l of that water (shown in red) for various times. t = 0s

t = 1s

t = 5s

t = 6s

Smaller pipe cross -sectional area means greater speed as long as the current is the same.

Conservation of Matter can tell is about fluid speed

(fluid speed is indicator for KE term)

I1 I2

A1v1 = A2v2 continuity equation

(just a matter of conserving matter…)

I1 = I2

Our Model for Analyzing Fluid Flow

(use these two ideas to analyze every fluid problem)

(1) Conservation of Energy (as applied to Fluids)

a.k.a. Fluid Transport Equation

Don’t’s : Since the fluid is in a steady state, you don’t pick two points in time to find the changes. Do’s : Instead, pick two points in the fluid circuit to calculate changes in the various quantities.

(P2– P1) + (1/2)(v22 – v1

2) + g( h2 – h1) + IR12 = 12

IR12: Resistance of the pipe between points 1 to 2

12: total energy/volume put in (or taken out) by all the pumps between points 1 to 2

(1) Conservation of Matter (as applied to Fluids)

a.k.a. Continuity Equation

I1 = I2, A1v1 = A2v2

Note :Closed circuits

When you return to the same place in the circuit, ∆P, ∆v2 and ∆h are zero!

Therefore the fluid transport equation reads

IRtotal = all

a.What is the energy density the pump adds to the fluid?b.What is the resistance of the pipe Rnarrow?

1 m3/s

R=0PA=101,300 PaPB=101,100 Pa

Rnarrow = ????

AABB

Below is a fluid circuit that lies flat on a tabletop. The pipe has no resistance and is the same diameter all the way along, except for a one section of narrow pipe. A steady current flows at 1 m3/s. The pressure at point A is 101,300 Pa and at point B it is 101,100 Pa. Use the above information to answer the following questions:

a)Use the fluid transport equation, starting at B and ending at A.

We know that

1 m3/s

PA=101,300 PaPB=101,100 Pa

Rnarrow = ????

AABB

•The heights are the same: hA = hb (i.e. hA - hB = 0)

• The velocities are the same: vA = vB • The resistence along the pipe from B to A is zero• There is one pump in the pipe from B to A

start end

path under consideration

a)

1 m3/s

PA=101,300 PaPB=101,100 Pa

Rnarrow = ????

AABB

i.e. The pump adds 200 Joules per cubic metre of energy to the fluid.

path under consideration

b)Use the fluid transport equation, starting at A and ending at B.

We know that

1 m3/s

PA=101,300 PaPB=101,100 Pa

Rnarrow = ????

AABB

•The heights are the same: hA = hb (i.e. hA - hB = 0)

• The velocities are the same: vA = vB • The resistence along the pipe from A to B is Rnarrow

• There are no pumps in the pipe from A to B

startend

path considered

b)

1 m3/s

PA=101,300 PaPB=101,100 Pa

Rnarrow = ????

AABB startend

path considered

Take home messages:

• The energy (density) gained through the pumps was 200 J/m3. The energy lost to thermal energy is IR = (1 x 200) = 200 J/m3.

• These numbers had to be the same, as there is no change between a point and itself!

• We only include resistors between the points of interest; not all resistors in the circuit.

• We only include pumps between the points of interest; not all the pumps in the circuit.

ElectricalElectrical circuits ! circuits !

How else is our Steady-State Energy Density Model useful?

What flows in it?Electricity seems mysterious because we cannot touch it or see it.

However, electricity is no more than a flow of charge from one point to the other.

Positive charge travels this way

We are going to model the motion of positive charges in a way analogous to how we treated water molecules

I Current charge/time, [I] = [Ampere] = [ coulomb/sec]

Parameterising our ignornance

• Charged particles in circuits feel very strong forces (electric forces). These forces are so strong that that we can safely neglect kinetic energy and gravitational potential energy.

• In a fluid system, pressure was the energy stored in the fluid per unit volume.

• In circuits, the voltage is the energy stored per unit charge. We have not developed a good idea for where voltage comes from (it involves electric forces, which we do not see until 7C), but we can still use it provided we just accept that charge leaving a battery has a different voltage

+-

+-

Ideas

FluidsFluids ElectricityElectricityDeals with Fluid flow Charge flow

CurrentWater flowing

through a cross-section of pipe per

unit time

Electric charge flowing through a wire per unit time

v Indicator of kinetic energy

(neglected)

hIndicator of

gravitational potential energy

(neglected)

R Relates current and thermal energy loss

Relates current and thermal energy loss

“Push” Pressure Voltage

Fluid transport equationAs applied to electrical circuit (V2– V1) + IR12 = 12

Conventions:Batteries are shown as a pair of lines, the longer of which is

the positive terminal.

Normal wires are shown as a solid line. These have resistance, but it is so small we neglect it.

Things with high resistance are indicated by a zigzagging line, or in the special case of lightbulbs

+-

resistor lightbulb (special resistor)

Current (charge) conservationJust like the number of water molecules does not change, the

number of charges do not change. As the charges push each other along, they cannot build up indefinitely.

Current in = current out

1 2 3

From rest of circuit

To rest of

circuit

I1 = I2 = I3, as the current cannot change and there is nowhere else for it to go

Current in = current out

From rest of circuit

To rest of

circuit1

2

3

4AA BB

Current into A = I1Current out of A = I2 + I3

Current into B = I2 + I3Current out of B = I4

II11 = I = I22 + I + I33

II22 + I + I3 3 = I= I44 = = II11

Current (charge) conservation

Important!

From rest of circuit

To rest of

circuit1

2

3

4AA BB

Never apply the electric transport equation directly between points 1 and 2!(They have different currents, so you don’t know which I to use)

Instead, we would use the fact that the voltage drop VB - VA is a fixed value, so it cannot depend on how we get from A to B.

If we know the resistances, we can use this and conservation of current to find the current through each resistor.

Next weekApril10 Lecture 2

Quiz1(20min) will cover:Today’s lecture (exclude electric circuit)Activities through DLM2 and FNTs from

DLM1Bring Calculator!

Closed-book, formulas will be provided.

DLM2&3 :

Steady-State Density Model applied to Fluid/Electric Circuits